In any part human operated machinery environment, in industrial and other environments, it is important for the machinery to avoid collisions with other objects. One important example of such an environment is in an open cut mining excavation environment.
FIG. 1 depicts a mining shovel loading a haul truck. This is a common activity in open-cut mining, but one which carries the significant risk of collision between the shovel and the truck. It would be desirable to have a technology that assists operators of earth-moving equipment to avoid such collisions. However, the need for such a technology arises in more or less the same form in several teleoperation contexts including nuclear decommissioning (Thompson et al. 2005, McAree & Daniel 2000, Daniel & McAree 2000, 1998) and space applications (Sheridan 1993). The aim is to filter the operator command so that the operator's intent is realized while avoiding collisions between the slave and obstacles in its workspace. The problem is characterized by (i) the presence of a human-in-the-loop who provides a command reference to the slave manipulator to achieve some defined task; (ii) significant energy associated with motion of the slave, with a high likelihood for damage-causing impacts between it and obstacles within its workspace; (iii) rate and saturation constraints on inputs states and outputs which limit the rate at which energy can be removed from and injected into the slave; (iv) the slave and workspace obstacles having non-convex geometries; and (v) a requirement for the slave to manoeuvre within concavities of obstacles.
Previous relevant work includes potential-field avoidance methods (Khatib 1986), motion planning (Latombe 1991, LaValle 2006), receding horizon trajectory planning (denoted RHTP) (Bellingham et al. 2002, Richards et al. 2003, Kuwata 2007, Kuwata et al. 2007) and set-theoretic control methods (Raković & Mayne 2005, Blanchini et al. 2004, Raković & Mayne 2007, Raković et al. 2007). Potential field obstacle avoidance methods were first explored in Khatib (1986) and have been applied frequently to obstacle avoidance problems, see for example (Latombe 1991, LaValle 2006, Ren et al. 2006, Barraquand et al. 1992). These methods use potential fields around each obstacle to determine planning or control laws that repel the manipulator. The approach, while conceptually attractive, suffers from the drawback that the potential field does not explicitly take account of the dynamics and performance limitations of the manipulator. Careful crafting of the potential field is required to guarantee avoidance and ensure that no alteration occurs in situations where collisions will not occur, such as moving parallel to an obstacle face. Motion planning methods, by way of contrast, seek to find a path from an initial configuration of a robot to a desired configuration avoiding all obstacles en route. These methods are most commonly used in autonomous robotics (Latombe 1991, LaValle 2006). The main differences between the motion planning and avoidance filtering problems is the objective and the available information: the final goal of the robot is known in the motion planning problem, hence the problem is fully specified, while for the avoidance filtering problem future commands are not known, and the objective is to minimize the alteration from the operator's command.
RHTP, for example, calculates the path to the goal configuration using a receding horizon control framework with the property that each time step, the minimum-cost trajectory to the goal configuration is computed and the first action is taken. This control structure allows for changes to the environment and the goal configuration to occur during the operation. RHTP can be implemented for polytopal obstacles, polytopal system constraints and linear (or piecewise afine) dynamics using MIP, see for example (Bellingham et al. 2002, Richards et al. 2003, Kuwata 2007, Kuwata et al. 2007). Set-theoretic control methods (Blanchini & Miani 2008) have also been applied to obstacle avoidance problems. Dynamic programming-based set iterates, for instance, have been used to robustly drive the state to the origin while avoiding obstacles (Rakovic & Mayne 2005), and linked invariant sets have been used to solve the obstacle avoidance with tracking problem (Blanchini et al. 2004). Both of these methods solve variations of the motion planning problem and, as such, are applicable to the avoidance filtering problem (Kearney et al. 2009). Set-theoretic methods were not considered because any change to the environment requires the re-computation of the sets which define the avoidance control laws, restricting these methods to a static environment. This attribute of set theoretic methods are not compatible with the level of detail strategy necessary to represent non-convex obstacle sets.